PLT OF SMT TWIN ENG TURBOPROP ACFT TOOK EVASIVE ACTION DURING LNDG AT A NON CTLED ARPT TO AVOID COLLIDING WITH ANOTHER ACFT TAKING OFF ON AN INTERSECTING RWY. NMAC;

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DEPARTED KENDALLVILLE; IN; FOR SMITH FIELD; IN. APPROX DISTANCE 20 MI WORKING WITH FT WAYNE APCH CTL FOR TA INTO SMITH FIELD FT WAYNE. WIND CONDITIONS AT FT WAYNE APPROX 8 MI S OF SMITH FIELD. THEY RPTED WINDS 050 DEGS AT 8 KTS. APPROX 5 MI N OF SMITH FIELD; I SWITCHED TO UNICOM AT SMITH FIELD; ADVISING TFC OF MY POS AND MY INTENTIONS TO ENTER A L DOWNWIND ENTRY FOR RWY 5. I CALLED A POS RPT ENTERING DOWNWIND FOR RWY 5. A SINGLE ENG ACFT WAS DEPARTING RWY 31. I INFORMED OF MY INTENTIONS FOR LNDG ON RWY 5. HE STATED HE SAW ME AND WOULD FLY A WIDE PATTERN FOR RWY 31. AT THAT TIME I HEARD NO OTHER TFC. I CALLED MY POS TURNING L BASE FOR RWY 5 AND I CALLED TURNING FINAL FOR RWY 5. AT JUST ABOUT TOUCHDOWN I SAW AN SMA TWIN ON THE ROLL ON RWY 31. I TRIED TO TALK WITH HIM BUT GOT NO RESPONSE BEFORE HE GOT TO THE INTXN AND AFTER HE ROTATED. IN ORDER TO AVOID A COLLISION AT THE INTXN I APPLIED BRAKES AND WENT INTO FULL REVERSE THRUST. THE L TIRE SMOKED AND THE RESULT WAS A FLAT SPOT ON THE TIRE. THERE WAS NO WAY I WAS IN ANY POS TO GAR. I FEEL THE BEST EVASIVE ACTION WAS TAKEN. THE ACFT WAS EITHER NOT ON THE UNICOM FREQ OR VOLUME WAS TURNED DOWN. ALTHOUGH I NEVER HEARD RADIO CALLS FROM HIM OR SAW HIM ON THE DEP END OF RWY 31. THE PERSON MONITORING UNICOM WAS AWAY FROM THE UNICOM AT THE TIME OF PATTERN ENTRY AND LNDG.